X-ray Spectra from
Magnetar Candidates
A Twist in the Field
R Turolla
Department of Physics
University of Padova, Italy
Credits
GL Israel, S. Mereghetti,
L Nobili, N Rea, N Sartore,
L Stella, A Tiengo, S Zane
Magnetic Fields and Neutron Star
Surface - Cocoyoc 14 February 2007
Galactic NS Population
 Present supernova rate in the Galaxy ≈
0.01 yr -1
 The Galaxy is ≈ 10 Gyr old
108 –109
neutron stars
 Most neutron stars are known through
their pulsed radio-emission
 Galactic pulsar population ≈ 105 (> 1500
detected)
Magnetic Fields and Neutron Star
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Pulsars and…
 The majority of neutron stars are old, dead
objects
 Observations in the X- and γ-rays revealed the
existence of populations of radio-quiet neutron
stars
 X-ray binaries
 X-ray dim isolated neutron stars
 Soft γ-repeaters
ISOLATED
 Anomalous X-ray pulsars
Magnetic Fields and Neutron Star
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Soft Gamma Repeaters - I
Rare class of sources, 4 confirmed (+ 1): SGR
1900+14, SGR 1806-20, SGR 1627-41 in the
Galaxy and SGR 0526-66 in the LMC
 Strong bursts of soft γ-/hard X-rays: L ~ 1041
erg/s, duration < 1 s

Bursts from SGR 1806-20 (INTEGRAL/IBIS,,Gőtz et al 2004)
Magnetic Fields and Neutron Star
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Soft Gamma Repeaters - II


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
Much more energetic “Giant Flares” (GFs, L ≈
1045-1047 erg/s) detected from 3 sources
No evidence for a binary companion, association
with a SNR in one case
Persistent X-ray emitters, L ≈ 1035 erg/s
Pulsations discovered both in GFs tails and
persistent emission, P ≈ 5 -10 s
Huge spindown rates, Ṗ/P ≈ 10-10 ss-1 (Kouveliotou et
al. 1998; 1999)
Magnetic Fields and Neutron Star
Surface - Cocoyoc 14 February 2007
Anomalous X-ray Pulsars - I





Seven sources known (+ 1 transient):
1E 1048.1-5937, 1E 2259+586, 4U 0142+614,
1 RXS J170849-4009, 1E 1841-045, CXOU
010043-721134, AX J1845-0258 (+ XTE J1810197)
Persistent X-ray emitters, L ≈ 1034 -1035 erg/s
Pulsations with P ≈ 5 -10 s
Large spindown rates, Ṗ/P ≈ 10-11 ss-1
No evidence for a binary companion,
association with a SNR in three cases
Magnetic Fields and Neutron Star
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Anomalous X-ray Pulsars - II

Bursts of soft γ-/hard X-rays
quite similar to those of
SGRs (AXPs much less active
though, bursts from two
sources only)
Woods &
Thompson
(2005)
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Time (sec)
A Tale of Two Populations ?
SGRs: bursting
X/γ-ray sources
AXPs: peculiar class
A Magnetar
of steady X-ray
sources
Single class of
objects
R < ctrise ≈ 300 km: a compact object
Pulsed X-ray emission: a neutron star
Magnetic Fields and Neutron Star
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Magnetars
Strong convection in a rapidly rotating (P
~ 1 ms) newborn neutron star generates a
very strong magnetic field via dynamo
action
 Magnetars: neutron stars with surface
field B > 10 BQED ~ 4 x1014 G (Duncan &
Thomson 1992; Thomson & Duncan 1993)
 Rapid spin-down due to magneto-dipolar
losses, P  1011 ( B / 1014 G) 2 P 1 ss 1

Magnetic Fields and Neutron Star
Surface - Cocoyoc 14 February 2007
Why magnetars ?

.LX  E rot  I
SGRs+AXPs
SGRs + AXPs
 No evidence for a companion star
High-field PSRs
 Spin down to present periods in ≈ 104
yrs requires B > 1014 G
PSRs
 Large measured spin-down rates
SPIN - DOWN ENERGY LOSS
 Quite natural explanation for the bursts
X-RAY LUMINOSITY

Magnetic Fields and Neutron Star
Surface - Cocoyoc 14 February 2007
SGRs and AXPs X-ray Spectra - I

0.5 – 10 keV emission well represented by
a blackbody plus a power law
AXP 1048-5937 (Lyutikov & Gavriil 2005)
SGR 1806-20 (Mereghetti et al 2005)
Magnetic Fields and Neutron Star
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SGRs and AXPs X-ray Spectra - II
kTBB ~ 0.5 keV, does not change much in
different sources
 Photon index Г ≈ 1 – 4, AXPs tend to be
softer
 SGRs and AXPs persistent emission is
variable (months/years)
 Variability mostly associated with the nonthermal component

Magnetic Fields and Neutron Star
Surface - Cocoyoc 14 February 2007
Hard X-ray Emission
INTEGRAL revealed
substantial emission in
the 20 -100 keV band
from SGRs and APXs
Mereghetti et al 2006
Hard power law tails
with Г ≈ 1-3, hardening
wrt soft X-ray emission
required in AXPs
Hard emission pulsed
Magnetic Fields and Neutron Star
Surface - Cocoyoc 14 February 2007
Hardness vs Spin-down Rate
Correlation between
spectral hardness
and spin-down rate
in SGRs and AXPs
(Marsden & White 2001)
Correlation holds
also for different
states within a
single source (SGR
1806-20, Mereghetti et al
2005; 1 RXS J1708494009, Rea et al 2005)
Harder X-ray
spectrum
Larger Spin-down rate
Magnetic Fields and Neutron Star
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SGR 1806-20 - I
SGR 1806-20 displayed a gradual
increase in the level of activity during
2003-2004 (Woods et al 2004; Mereghetti et al
2005)
Bursts / day
(IPN)
 enhanced burst rate
 increased persistent luminosity
20-60 keV flux (INTEGRAL IBIS)
The 2004 December 27 Event
Spring
2003
Autumn
2003
Spring
2004
Autumn
2004
Mereghetti et al 2005
Magnetic Fields and Neutron Star
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SGR 1806-20 - II






Four XMM-Newton observations (last on
October 5 2004, Mereghetti et al 2005)
Pulsations clearly detected in all observations
Ṗ ~ 5.5x10-10 s/s, higher than the “historical”
value
Blackbody component in addition to an
absorbed power law (kT ~ 0.79 keV)
Harder spectra: Γ ~ 1.5 vs. Γ ~ 2
The 2-10 keV luminosity almost doubled (LX ~
1036 erg/s)
Magnetic Fields and Neutron Star
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Twisted Magnetospheres – I
The magnetic field inside a magnetar is
“wound up”
 The presence of a toroidal component
induces a rotation of the surface layers
 The crust tensile strength resists
 A gradual (quasi-plastic ?) deformation of
the crust
 The external field twists up (Thompson,

Lyutikov & Kulkarni 2002)
Magnetic Fields and Neutron Star
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Thompson & Duncan 2001
Twisted Magnetospheres - II

TLK02 investigated
force-free magnetic
 
equilibria ( J  B  0)
 

   B   ( R,  ) B

A sequence of models
labeled by the twist
angle

 N  S  2 2
0
B d
B sin 
Magnetic Fields and Neutron Star
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Twisted Magnetospheres - III





Twisted magnetospheres are threaded by
currents
Charged particles provide large optical depth  rs
to resonant cyclotron scattering
Because c  c ( R, ) and Rcurrent  RNS , a powerlaw tail expected instead of an absorption line
Btwist  R  ( 2 p ,) Bdip  R 3 and Ptwist  Pdip
Both  rs and Ptwist increase with the twist
angle
Magnetic Fields and Neutron Star
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A Growing Twist in SGR 1806-20 ?
Evidence for spectral
hardening AND
enhanced spin-down
 and   L
 P
correlations
 Growth of bursting
activity
 Possible presence of
proton cyclotron line
only during bursts

All these features are
consistent with an
increasingly twisted
magnetosphere
Magnetic Fields and Neutron Star
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A Monte Carlo Approach
Follow individually a large sample of
photons, treating probabilistically their
Preliminary
investigation
(1D)
by Lyutikov
interactions
with
charged
particles
Basic ingredients:
&
Gavriil
(2005)
 Can
handle
general
(3D) geometries
 Space
andvery
energy
distribution
of the
More detailed modeling by Fernandez &
scattering
 Quite
easy toparticles
code, fast
Thompson (2006)

Same
for
the
seed
(primary)
photons
New,
Ideal up-to-dated
for purely scattering
media
code (Nobili,
Turolla,
 Scattering cross sections
Zane
Monte
techniques
& Carlo
Sartore
2007) work well when
Nscat ≈ 1

Magnetic Fields and Neutron Star
Surface - Cocoyoc 14 February 2007
Select seed photon
(energy and direction)
Generate a uniform
deviate 0<R<1
No
No
Select particle from distribution
Transform photon
energyphoton,
and direction to ERF
Advance
   ln R ? 2
Escape Compute
?
photoncompute
energy after
depthscattering  '   /[1   (1  cos )]
Compute new photon direction
 
 
Yes
2
cos '
R '   d '
0
1
d ' d ( , k , k ' ) / d' /  d' d ( , k , k ' ) / d'
Transform back to LAB
Compute scattering
Yes
4
Store data
Magnetic Fields and Neutron Star
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Magnetospheric Currents
 
 Charges move along the field lines v B

Spatial distribution
1
p  1  B

n
4e  B
-3
 B p  RNS 
 14  only cm
 10 contribution
Electron
G  10 km 
 10 Mawellian
1D relativistic
at
 Particle motion characterized
Te centred at vbulk
16
 cB

 r vbulk
by a bulk
velocity, vbulk, and by a velocity spread Δv
(Beloborodov & Thompson 2006)

There may be e± in addition to e-p, but no
detailed model as yet
Magnetic Fields and Neutron Star
Surface - Cocoyoc 14 February 2007
Surface Emission
The star surface is
divided into patches
by a cos θ – φ grid
Each patch has its
own temperature to
reproduce different
thermal maps
Blackbody (isotropic)
emission
Magnetic Fields and Neutron Star
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Photons in a Magnetized Medium
Magnetized plasma is anisotropic and
birefringent, radiative processes sensitive
to polarization state
 Two normal, elliptically polarized modes in
the magnetized “vacuum+cold plasma”
14
2
2
3
 At   V  ( B / 10 G ) ( / 1 keV) gcm
the modes are almost linearly polarized

The extraordinary (X) and ordinary (O) modes
Magnetic Fields and Neutron Star
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Scattering Cross Sections - I
QED cross section available (Herold 1979, Harding &
Daugherty 1991) but unwieldy
 Non-relativistic (Thompson) cross section
(ε<mc2/γ≈50 keV, B/BQED < 1)

Completely differenti al cross sections at resonance (ERF)
3r0 c
d

 (  c ) cos 2  cos 2  '
d' O O
8
3r0 c
d

 (  c )
d ' X  X
8
3r0 c
d

 (  c ) cos 2 
d' O  X
8
3r0 c
d

 (  c ) cos 2  '
d ' X  O
8
r0  e 2 / mc 2 , c  eB / mc,  ,  ' angles between photon direction and particle
velocity before and after scattering
Magnetic Fields and Neutron Star
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Scattering Cross Sections - II
Because of charge motion resonance at
c
res 
 (1   cos  )
 For a given photon (energy ω, direction k)

  (c /  ) (c /  )    1
  res  1, 2 
(c /  ) 2   2
2
(1   i )
1
 (  res ) 
 (  i )

c i 1, 2  i    i
2
Magnetic Fields and Neutron Star
Surface - Cocoyoc 14 February 2007
2
Model Spectra - I
Model parameters: ΔΦN-S, Bpole, Te, vbulk
Surface emission geometry, viewing angle
hardness increases
Emission from entire star surface at Tγ=0.5 keV
1014 G
B  1014 G
B
 10
B G
10 G

N -S  0.7
14
14
 N -S N -S
B

100.G
7
14
 N -S  0.7
0.7
1015 G
B  1015 G
twist increases
N -S  1B.210
15
G
 N -S  1.2
Magnetic Fields and Neutron Star
Surface - Cocoyoc 14 February 2007
Model Spectra - II
Line of sight effects
Emission from a single patch at the equator
LOS
same
LOSat
atthe
opposite
longitude
longitudeof the patch
Magnetic Fields and Neutron Star
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Conclusions & Future
Developments
Twisted magnetosphere model, within magnetar
scenario, in general agreement with observations
 Resonant scattering of thermal, surface photons
produces spectra with right properties
 Many issues need to be investigated further

– Twist of more general external fields
– Detailed models for magnetospheric currents
– More accurate treatment of cross section including QED
effects and electron recoil (in progress)
– 10-100 keV tails: up-scattering by (ultra)relativistic (e±)
particles ?
– Create an archive to fit model spectra to observations
(in progress)
Magnetic Fields and Neutron Star
Surface - Cocoyoc 14 February 2007
Post-Flare Evolution
After the GF SGR
1806-20 persistent
X-ray emission is
softer and spindown rate smaller
 Evidence for an
untwisting of the
magnetosphere

Magnetic Fields and Neutron Star
Surface - Cocoyoc 14 February 2007
Part I: Observational Facts (mainly)
Part II: Theoretical Implications (and
Speculations…)
Soft Gamma Repeaters are
ULTRA-MAGNETIZED NEUTRON
STARS, i.e. MAGNETARS
Magnetic Fields and Neutron Star
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